Tuesday, March 4, 2014

Rational Functions And Killing Kittens

Did I get your attention with the title of my post? Before you call PETA on me, please read the rest of the post. I don't want to kill kittens. You could say I'm in the saving kittens business. Confused? Let me explain.

My Algebra 2 students just started one of our last units on rational functions. We're working on simplifying rational functions You know, factor everything. Cancel out factors, not terms. My students love, love, love to cancel out terms. Last year, I preached and preached about the difference between factors and terms. But, it didn't seem to do much good.

This year, I decided to take a different approach. I gave my normal spiel. Okay guys. Today, we're learning something new. Well, actually it's not entirely new. We're going to combine lots of stuff we've done before to do something we've never done before. Now, before we start, I want to warn you of an important rule. You can only cancel out factors. Factors are things that are being multiplied. You may never cancel out terms. Terms are things that are being added.

By this time, the eyes of almost everybody in class have glazed over. Or, they're talking to their neighbors. Or, they're trying to text somebody without me noticing. I realize they haven't heard a word that I've said. That's okay. I expected this. I was prepared for this.

Cue the next slide in my SMART Board file.

Rational Functions - Every time you do this, a kitten dies.

All of a sudden, I have the attention of my class. There is an audible gasp. Comments are made about how horrible of a person I am for wanting to kill a kitten. Eventually, a student asks, "Why would doing that cause a kitten to die?" Oh, I'm so glad that you asked! I hit the back button to return to my slide that talks about the difference between factors and terms. I once again remind them that they are only allowed to cancel out factors, not terms. We return to the slide with the adorable kitten. Are the x squared terms factors or terms? They are being added, so they are terms. And, we never, ever, ever cancel out terms!

Want a copy of this image or others to use with your students? I downloaded this from Math Curmudgeon.

Some of the shock wears off. A few students nod their heads as if they understand. One student asks if she can take a picture of the screen before we move on. Sure!

And, this is how I became Insta/facebook famous. I love the hashtag. #savekittens

Facebook / Instagram Post

Students posting about math on social media? I can handle this.

We move on to practice problems. I put up a rational expression on the SMART Board. Students attempt to simplify it on their mini dry erase boards. They hold up their work for instant feedback. I continually warn them. Factor everything first. This allows you to cancel factors! Please, please, please don't try to cancel out terms. Remember, every time you cancel terms, a kitten dies. And, if you try to cancel out terms, I will be forced to draw a dead kitten on the board.

We do well until we get to this problem: (35x-35) / (25x - 40). With some prompting, the students successfully factor out a five from the numerator and denominator and cancel them out. Then, another student suggests that we cancel out the x's.

Oh no!!!!! You just killed a kitten. The x's are terms, not factors. Oh no!!!!!!! Now, I'm going to have to draw a dead kitten on the board. I warned you this would happen. You should have been more careful.

By this point in the year, my students are very well aware of the fact that I cannot draw. So, they are eagerly awaiting to see what this dead cat will look like. I hadn't exactly planned this far ahead, so I'm eager to find out what my drawing will look like, too.

After I draw the cat, I have a dilemma. How in the world am I going to make this a dead cat?!? I don't want to do something too gruesome. Eventually, I settle on a red x through my cat. That should get the point across. My students are pleasantly surprised with how good my cat turned out. Though, they protest that the cat shouldn't be smiling since it's dead. I'm sorry. I've never drawn a dead cat before. And, this is the only way I know to draw a mouth on a cat.

My Attempt at Drawing a Dead Kitty

Another student decides we need a more permanent memorial to the cat our class has sacrificed today with our carelessness. She draws a cat and balances the dry erase board above my bulletin board. She even gives it a name. Pablo. Died February 28, 2014.

Poor Kitty - Met Its Demise At The Hand Of My 2nd Hr Algebra 2 Students & Their Careless Canceling

My afternoon Algebra 2 class comes in. Why is there a cat on the wall? You'll find out. I give them an even more impassioned plea. 2nd hour killed a kitten. They killed a cat! Can you believe it? I was forced to draw a dead cat on the board as a result. Please don't make me go through that nightmare again! Please, don't kill a cat. Only cancel factors, not terms. My fifth hour is much more careful of their canceling. No kittens were killed during our first 50 minutes of simplifying. I can only hope that streak continues.

I'll be honest. This unit is less than spectacular. I feel like I'm on a race to the finish with end-of-instruction exams coming up in less than 20 school days. We haven't done a single notebook page this chapter which is DEFINITELY not like me!

I'm just always curious to see what other people are doing. The texts we have are horrible (I haven't touched them in 7 years and they were new 10 years ago when I was hired) and we do a lot of supplementing. I'm sitting on our book adoption committee and we can't wait to get our hands on all of the resources that the books we're looking at have. I used the kitten picture with my students today. It helped them think about the difference between a factor and a term.

Our textbooks are horrible, too. My district keeps rebuying the same textbook so they can keep reusing the old textbooks. When they hired me two years ago, they placed a order for new Alg 1 books without asking me if that was what I wanted. They are sitting in my cabinet, brand new. I completely understand your frustration!

What seems to be working this time is that I taught them that + and - signs indicate that a variable and a number (or whatever) are a married couple. If you try to reduce one member of a married couple you are acting like a home wrecker. I know. It's bad.

However, I am amazed at how well they remember it. I'll hear shouts of: "Stop it, you are being a home wrecker! We have to factor first." across my room. Priceless. Seriously.

However, if you separate them first (factoring or writing each term separately over its own denominator, it is a legal separation and the next step is divorce. I know it is bad, but it seems to resonate with them.

Have you seen the dead puppy theorem for exponents. "Every time you do this: (x + 3)^2=x^2+9 a puppy dies" I go over it when we look at exponents and if they do it, I write dead puppy on their paper. I asked on my end of the year survey in Algebra 2 "what will you do to be successful in the math class you take next year?" And one kid put "I won't kill puppies." :) it's amazing how some things stick!

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